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Mata kuliah Analisis Reaktor Nuklir , bahan ajar Dr-Ing Sihana
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Department of Engineering Physics, Faculty of Engineering, Gadjah Mada University (Study Programs of Engineering Physics & Nuclear Engineering)
Jl. Grafika 2, Yogyakarta 55281, (+62 274) 580882, http://www.tf.ugm.ac.id/
Nuclear Fission
2011
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Fission Reactions
Spontaneous Fissiono Most heavy nuclei decay by -emission.o Some can also spontaneously fission:
• 252Cf (2.638 y; fission prob. 3.09%).• 250Cm (6900 y; fission prob. 61.0%).
Neutron Induced Fissiono Neutron can induce fission:
• Produce a COMPOUND NUCLEUS.• Highly Excited State• One of the decay modes is FISSION.
2
1 2350 92
235 192 0
235 192
236 *9
0
23
2
H y 1
692
2
n + U
U + n elastic scatter
U + n´+ inelasticscatter
U + radiativecaptu
U
Y + Y + y + y + fissio
re
n
Possible neutron Interactions with U-235
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Fission Reactions
Neutrons are released in Fission Reactionso The fission products are “neutron rich”.o Some of the subatomic particles emitted (y1,y2,…) are neutrons: chain reaction.o Self sustaining fission reaction releases fission energy.
Fission depends on Neutron Energy:o Fission at very low energy (thermal ~0.025 eV): FISSILE NUCLEI.
• 235U, 233U, 239Pu.
o Fission at higher energies (MeV): FISSIONABLE NUCLEI.• 238U, 240Pu.
Conversion to Fissile Nuclei (BREEDING):o Nuclei can be converted to fissile nuclei by absorbing slow neutrons.
3
232 233233 *90
239 *92
10 22 m 290 91 92
92 93
233
238 239
7 d
10 24 m 56 h 9
2 94
3
Th + n Pa UTh
U + n Np PuU
232Th and 238Uare FERTILE nuclides
232Th and 238Uare FERTILE nuclides
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Characteristics of the Fission ReactionScission Explained by the “Liquid Drop”
Model• Compound Nucleus Highly Excited.• Large oscillations of shape of “Nuclear
Fluid”.• Elongated shape breaks in two (10-20s):
Primary Fission Products YH, YL
• Highly Excited States.• Neutrons “evaporate” from surface (10-17
s): PROMPT NEUTRONS p.• Reduce excitation by emission (~10-14
s): PROMPT GAMMAS p.
Fission Fragments Transfer Kinetic Energy to the surrounding medium in ~10-12 s.
4
Coulomb Repulsion >> Nuclear ForcesCoulomb Repulsion >> Nuclear Forces
14
20
-17
-14
1 2350 92 10 s
** **
10 s
Prompt Neutrons** *
235 *92
* * *
10 s
Prompt Gammas* *
10 s
10
n + U SCISSION
SCISSION (Y ) +(Y ) +( )
(Y ) +(Y ) (Y ) +(Y )
(Y ) +(Y ) Y + Y +
Y
(
U
n)
n mH L
n m n mH L H L
n m np
mH L H L
nH
p
n m e
-12
KETrans
10
fer
s+ Y +( ) Y + Ym
L H Ln m e
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Fission Products
Fission Product Decay Chainso Several Hundred different nuclides can be
producedo They are all neutron rich and decay by -
emission until a stable nuclide is reached: DECAY CHAIN.
Important Decay Chains
5
- - - -140 140 14054 55 58
16 s 66 s 18.8 d 4
140 14056 7
0 h5Ba LXe Cs Ce(stable)a
Hahn and Strassman discovered fission
- -147 1160 1 2
11d 2.
147 14761 62
6 yPm SmNd (T =10 y)
Characterization of Promethium and production of Samarium. Very effective thermal neutron absorbers
- - - - -
-
99 99 99 99 9938 39 40 41 42
0.27 s 1.5 s 2.2 s 15 s 2.
9
75 d
9944
6.01 h 0.21 M
994
93 3
*
y4
Sr Y Zr Nb Mo
Ru (stabl )T Tc ecm
Discovery and Production of Technetium for medical applications
- - - - -13554
135 135 135 135 13551 52 53 55 56
1.7 s 19 s 6.57 h 9.10 h 2.6 MyXeSb Te I Cs Ba (stable)
Production of Xe-135, largest low energy neutron absorption X-section
- - -
-
1 2
stab
X X X
X ( l )e
A A AZ
n
Z Z
AZ
23592
1.2 1.4
for U( )
to for stable Fission Pro
1.57
ducts
A Z
Z
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Fission Products
Mass Distribution of Fission Products
o The mass of fission fragments ranges from 70 to ~170.
o 100 different fission chains (with constant A) are formed.
o Fission Chain Yield y(A):Probability a fission fragment is a nuclide with
mass number A.
o The fission yield curve is ASYMETRIC• It depends on the fissioned nuclide.• It depends on the Neutron Energy: higher energy,
less asymmetry.6
Compound NucleusH L pA A A
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Fission Products
Initial Energy of Fission Fragmentso The kinetic energy of the two fission
fragments must equal: • The kinetic energy of the neutron and
• The Q-value of the fission reaction.
o For a fission induced by a thermal neutron:• Conservation of Momentum
• The sharing of Kinetic Energy is:
7
or L LL L H H
H H
v mm v m v
v m
212
212
L LL
H H
H
H L
m v
m v
E m
E m
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Neutron Emission in Fission
• Prompt Neutrons:• Released within 10-14 s.
• Number p can vary from 0 to 8.
• The average number is for thermal fission depends on nuclide and neutron energy.
• Delayed Neutrons:• Small fraction (1% Thermal) of neutrons are
emitted as delayed neutrons.
• The come from the Decay of Fission Products.
• The time is from some seconds to minutes.
• The average number depends strongly on:Fissioning nucleus.Energy of the inducing neutron.
8
2.5p Average Number of PROMPT Neutrons
DELAYED Neutron Fraction d
p d Average TOTAL Number of Neutrons
DELAYED Neutrons are ESSENTIAL to control the
Nuclear Reaction
DELAYED Neutrons are ESSENTIAL to control the
Nuclear Reaction
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Delayed Neutron Emission
9Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Neutron Emission in Fission
10
( )
2
4( ) sinh
w wE E Tw
ww w
E EeE
TE T
The neutron energy distribution is a continuous Maxwellian Distribution which depends on:
•Material (Tw and Ew)•Neutron Energy: E
The AVERAGE energy is ~ 2 MeV
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Prompt Energy Released
• The amount of energy per fission can be estimated by using the BINDING energy per NUCLEON.
• Energy is released in TWO TIME SCALES:
• Prompt (10-12 s): Kinetic Energy.Prompt Neutrons.Prompt Gammas
• Delayed (s to minutes): Decay of fission Products.
11
235 1 140 * 96 *92 0 54 38
after 140 96 154 38 0
1s
U + n Xe + Sr
Xe + Sr + 2( n) +7( )
235 139 95 292 54 38( U) ( Xe) ( Sr) 2p n nE M m M M m c
[235.043923 1.008665 138.918787
94.919358 2(1.0086659)]uma 931.5MeV/uma
pE
183.6MeVpE
183.6MeV -5.2MeV -6.7 MeV 171. MeV= 7KE
6.7 MeV
5.2 MeV
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Energy from Fission Productso Most Fission Products decay in a
few years.o Some others have much larger
half-lives.o The Decay Heat is of concern for:
• Nuclear Safety: Removal of Decay Heat.
• Management of Spent Fuel.o Calculations based on Empirical
Models:
12
1.2 1 1
1.2 1 1
5
( ) 1.4 MeV s fission
( ) 1.26 MeV s fission
in s after fission (10 s < < 10 s)
F t t
F t t
t t
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Delayed Energy Released
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139 13995 9538 42
0 01 154 57Xe L+ 7( ) + +7(a ) +7( )Sr Moe
[138.918787 94.919358 138.906348 94.905842 93]uma 1.5MeV/umadE
139 95 139 95 254 38 57 42( Xe) ( Sr) ( La) ( Mo)dE M M M M c
24.2MeVdE
Anti-neutrinoDecay Chains
Energy = Mass Defect c2
Delayed Fission Energy Released
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Energy Released in Fission
14Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Energy Released in Fission• How Much U-235 has to fission to generate 1 MWd ?
15
013
11 11W =1 J/s
1.602 10 J/MeV 2003.1
M10 fissio
eV/fissin/s
on
216
3
2351MW = fission/s 86400s/d g/atom-fissioned =1.05g/d
6.3.1
023 1010
23592
With only 85% of captures ending up in
1.24 g of
fission
1 MWd U cons= umed.
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Nuclear Fission Chain ReactionA Fissile atom (e.g 235U) absorbs a neutron, and:
• fissions in two new atoms (fission fragments),
• releasing three new neutrons
• and energy.
The neutrons can be• Absorbed by an atom of 238U (or other absorber),
and does not continue the reaction: ABSORPTION.
• Lost and does not collide with anything: LEAKAGE.
• Collide with a fissile atom (e.g 235U) which then fissions and releases additional neutrons: CHAIN REACTION.
16
Leakage
2nd generation
3rd generation
1st generation
Non-FissionAbsorption
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The Neutron Cycle in a Thermal Reactor
17Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Quantification of the Thermal Cycle
1. The FAST Fission Factor o Most fast fissions take place in 238U (En > 1 MeV)o Natural or slightly enriched U cores: between 1.02 and 1.o8.
2. Resonance Escape Probability po Accounts for FAST neutron absorption during MODERATION.o p depends on the cross-sections in the resonance absorption region o For U fuelled reactors p varies depending on the moderator to fuel ratio:
higher ratio increases p (most absorptions take place in U-238.)
18
Total Neutrons Produced by FAST and THERMAL fissions
Neutrons by THERMAL fission
Probability that a Fast Neutron Slows down without being absorbed.p
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Quantification of the Thermal Cycle
3. Fast Non-Leakage Probabilityo Probability that a FAST neutron does not leak from the core during
moderation.o For a non-reflected core:
Leakage probabilities depend on:o Materials used in the Reactor: L (D, a), . L, increase Leakage increases.
o Geometry of the reactor: Buckling. Buckling increases Leakage increases
o Reactor Homogenous or Heterogeneous.
o Use of a REFLECTOR of NEUTRONS: Decreases Leakage.
19
fNLP
2cBf
NLP e is the Fermi age.
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Quantification of the Thermal Cycle
4. Thermal non-Leakage Probabilityo Probability that a thermal neutron does not leak out (escape) of the core
before it is absorbed.
• L is the thermal diffusion length: one-half of the average distance difussed by a thermal neutron before it is absorbed.
• Bc2 is the “Critical Buckling”: Related to the Geometry of the Reactor.
20
thNLP
2 2
1
1th
NLc
PL B
2aL D
Thermal Diffusion
Coefficient
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Quantification of the Thermal Cycle
5. The Thermal Utilization fo Not all thermal neutrons are absorbed by the fuel.o f is the Probability that the neutrons are absorbed by the fuel.
6. Thermal Fission Factor o Number of FAST neutrons produced per absorbed neutron in fuel.
21
F F Fa VNF NF NFa V
( ) ( )
NF NF NF
NF F NF
F F Fa
F F Fa
F
a
NFa
Fa
Fa
V
Vf
V
V V
Fuel Absorption rate
Non-Fuel Absorption rate
Ff
Fa
MUST be > 1 for a self sustaining chain reaction
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Quantification of the Thermal Cycle
22
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Quantification of the Thermal Cycle
Effective Multiplication Factor
Infinite Multiplication Factoro In an infinite medium there is no leakage.
23
no. neutrons at some point in the cycle
no. of neutrons at the same point in the previous cycleeffk
th fNL NL
eff
n p f P Pnk
n n
th feff NL NLk p f P P
1
1
1
eff
ef
f
f
ef
k Supercritical n n
k Sub
k Critical n
critical n n
n
k p f k∞ depends only on
the MATERIAL in the core
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Core Design Estimates
What fuel to use for a Thermal Reactor ?o Only Natural Uranium ?
• With 0.72 atom-% of 235U and ~99.3% of 238U.• The probability of resonace absorption is very high• p , the probability of escaping the resonance is very low.
• k∞ << 1.0.
o Reactor design solutions: • Increase p : Use an EFFECTIVE MODERATOR.• Increase f : Use more fissile material.• Increase : use a fuel with more neutrons per fission and low
24
f
th feff NL NLk p f P P
k p f
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Core Design Estimates
25
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
Increasing
But, there is no U-233 in Nature, one must “make” it.
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Core Design Estimates
Ifo There is too little moderator , is small, p is very small and
o There is too much moderator, is large, f is small and
o There is an optimal that gives a maximum for
26
Moderator
Fuel
N
N1.0k
Moderator
Fuel
N
N1.0k
Moderator
Fuel
opt
N
N
k
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
Only Heavy Water as a Moderator can be used for an homogeneous natural uranium reactor
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Quantification of the Thermal Cycle
27Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
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Core Design Estimates
So, how can we build a nuclear reactor with Uranium without Heavy Water as Moderator ?.
o Increase f• Increasing 235U content from 0.72 % to > ~ 2.5% : ENRICHMENT
• More fissile fuel will increase more chance of absorption by fuel.
AND/OR
o Increase p• Construct an HETEROGENEOUS core by separating fuel and moderator.
• More Fast neutrons escape the fuel
• They are thermalized away from 238U resonances more probability of escaping the resonances.
• Heterogeneous reactors also have a higher (more fast fissions in 238U).
28
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Core Design Estimates
29
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
HETEROGENEOUS CORE
Fuel
Moderator
Neutron moderation
fast
thermal
More Heterogeneous: f decreasesMore heterogeneous: p increasesThere´s an optimum for k∞ max
UGM
Dep
art
men
t of
En
gin
eeri
ng
Ph
ysi
cs, Fa
cult
y o
f En
gin
eeri
ng
S
tud
y P
rog
ram
s of
En
gin
eeri
ng
Ph
ysi
cs &
Nu
clear
En
gin
eeri
ng
Core Design Estimates
Finally, we have to take care of the LEAKAGE
o Increase • We surround the core with a material with a HIGH scattering-to-absorption cross section:
REFLECTOR.
30
th fNL N effLPk P k
andth fNL NLP P
Reflectors reduce LeakageReflectors reduce Leakage
Reflectors reduce Peak-to-average powerReflectors reduce Peak-to-average power
Reflectors reduce Fast Neutron Flux outside the core
Reflectors reduce Fast Neutron Flux outside the core
neutr
ons/
cm2 s
center
Source: J.K. Shultis and R.E. Faw, “Fundamentals of Nuclear Engineering”, Marcel Dekker, 2002
